Equitable Power Domination Number of Certain Graphs - Banu Priya, S.; Srinivasan, N. (International Journal of Engineering and Technology, 2018)
Let 12G"> be a graph with vertex set 12V"> , a set 12Sâٹ†V"> is said to be a power dominating set (PDS), if every vertex 12uâˆˆV-S"> is observed by some vertices in 12S"> using the following rules: (i) if a vertex 12v"> in 12G"> is in PDS, then it dominates itself and all the adjacent vertices of 12v"> and (ii) if an observed vertex 12v"> in 12G"> has 12k>1"> adjacent vertices and if 12k-1"> of these vertices are already observed, then the remaining one non-observed vertex will also be observed by 12v"> in 12G"> . The degree 12d(v)"> of a vertex 12v"> in 12G"> is the number of edges of 12G"> incident with 12v"> and any two adjacent vertices 12u"> and 12v"> in 12G"> are said to hold equitable property if 12|d(u)-d(v)| â‰¤ 1"> . In this paper, we introduce the notions of equitable power dominating set and equitable power domination number. We also derive the equitable power domination number of certain graphs.